grid.sim produce comparable output to mvnorm, however for methods 2 to 4 grid.sim make use of center and scaling, and or use a fix grid of values for one column of the output. The intended use of grid.sim is for computing confidence intervals (CI) for model predictions. Method 1 is the same as rmvnorm, however can handle cases of zero variances in sigma. Method 2 is method 1 followed by centering and scaling of the simulated matrix. Thus output when using method 2 always have sample mean and covariance equal to input parameters means and sigma. Method 3 is the same as method 1 however with one column having a fixed range of values rather than a simulated range of values. Method 4 is method 3 followed by centering and scaling of the simulated matrix. Thus output when using method 4 always have sample mean and covariance equal to input parameters means and sigma.
As the number of simulations (n) goes to infinity all methods in grid.sim are identical to mvnorm in that the sample covariance (mean) of the output will converge to the input covariance matrix sigma (vector means).
The advantage with methods 2 to 4 (over method 1 and rmvnorm) is that they provides more stable results, hence number of simulations can be reduced and still have equally stable results when used to represent parameter uncertainty and or population variability in model predictions.
grid.sim(n, means = NULL, sigma, grid.param = NULL, method = 4)row-matrix of parameters
Number of simulations
vector of mean values
covariance matrix
the index of the parameter for which a fix grid (from qnorm) is used instead of a simulated grid (rnorm). If grid.param=NULL (default) the fix grid will be used for the parameter with largest variance.
simulation method, default=4
sigma<-matrix(c(1,0.5,0.5,2),ncol=2)
sim1<-grid.sim(1000,sigma=sigma)
pairs(sim1)
cov(sim1)
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